Question

Write equilibrium constant \((K)\) expressions for the following reactions: (a) \(\mathrm{Na}_{2} \mathrm{CO}_{3}(s) \rightleftharpoons 2 \mathrm{NaO}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons 2 \mathrm{CO}(g)+5 \mathrm{H}_{2}(g)\) (c) \(4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g)\) (d) \(\mathrm{NH}_{3}(g)+\mathrm{HI}(l) \rightleftharpoons \mathrm{NH}_{4} \mathrm{I}(s)\)

Short answer

Question: Write the equilibrium constant expressions for the following reactions: (a) \(\mathrm{Na}_{2}\mathrm{CO}_{3}(s) \rightleftharpoons 2\mathrm{NaO}(s)+\mathrm{CO}_{2}(g)\) (b) \(\mathrm{C}_{2}\mathrm{H}_{6}(g)+2\mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons 2\mathrm{CO}(g)+5\mathrm{H}_{2}(g)\) (c) \(4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g)\) (d) \(\mathrm{NH}_{3}(g)+\mathrm{HI}(l) \rightleftharpoons \mathrm{NH}_{4} \mathrm{I}(s)\) Answer: (a) \(K=[\mathrm{CO}_{2}(g)]\) (b) \(K=\frac{[\mathrm{CO}(g)]^{2}[\mathrm{H}_{2}(g)]^{5}}{[\mathrm{C}_{2}\mathrm{H}_{6}(g)]}\) (c) \(K=\frac{[\mathrm{NH}_{3}(g)]^{4}[\mathrm{O}_{2}(g)]^{5}}{[\mathrm{NO}(g)]^{4}[\mathrm{H}_{2}\mathrm{O}(g)]^{6}}\) (d) \(K=\frac{1}{[\mathrm{NH}_{3}(g)]}\)

Step-by-step solution

(a) Write the equilibrium constant expression for \(\mathrm{Na}_{2}\mathrm{CO}_{3}(s) \rightleftharpoons 2\mathrm{NaO}(s)+\mathrm{CO}_{2}(g)\)

Since the concentration of solids is considered constant, only the \([\mathrm{CO}_{2}(g)]\) is accounted for in this equilibrium expression. Therefore, the equilibrium constant \((K)\) expression for reaction (a) is: \(K=[\mathrm{CO}_{2}(g)]\)

(b) Write the equilibrium constant expression for \(\mathrm{C}_{2}\mathrm{H}_{6}(g)+2\mathrm{H}_{2}\mathrm{O}(l) \rightleftharpoons 2\mathrm{CO}(g)+5\mathrm{H}_{2}(g)\)

In this case, we account for the concentrations of gases only, disregarding the liquid concentration. The equilibrium constant \((K)\) expression for reaction (b) is: \(K=\frac{[\mathrm{CO}(g)]^{2}[\mathrm{H}_{2}(g)]^{5}}{[\mathrm{C}_{2}\mathrm{H}_{6}(g)]}\)

(c) Write the equilibrium constant expression for \(4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g)\)

All components in this reaction are gases, so we account for the concentration of each species. The equilibrium constant \((K)\) expression for reaction (c) is: \(K=\frac{[\mathrm{NH}_{3}(g)]^{4}[\mathrm{O}_{2}(g)]^{5}}{[\mathrm{NO}(g)]^{4}[\mathrm{H}_{2}\mathrm{O}(g)]^{6}}\)

(d) Write the equilibrium constant expression for \(\mathrm{NH}_{3}(g)+\mathrm{HI}(l) \rightleftharpoons \mathrm{NH}_{4} \mathrm{I}(s)\)

Here, we neglect the concentrations of the liquid and solid components, only considering the gas concentration. The equilibrium constant \((K)\) expression for reaction (d) is: \(K=\frac{1}{[\mathrm{NH}_{3}(g)]}\)